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Likelihood Exploration Worksheet

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Likelihood Exploration Worksheet

A festival stall is planning a prize wheel. Use ratios to compare outcomes and make fair, evidence-based decisions. Simplify each ratio where possible. Show your working.

Part A: Read the chance

The spinner has 12 equal sectors: 6 blue, 3 yellow, 2 red and 1 green. Each sector is equally likely to be selected.

1.Write the ratio of blue sectors to yellow sectors. Give it in simplest form.

2.Which colour is most likely to be selected? Choose one and explain using a ratio of that colour’s sectors to all sectors.

3.What is the ratio of red sectors to green sectors? What does this tell you about their relative chances?

4.What is the ratio of sectors that are not yellow to all sectors? Simplify it.

Part B: Predict and test

Harrison spins the wheel 24 times. For a prediction, assume the results follow the wheel’s sector ratios.

5.Complete the expected-results ratios and counts for 24 spins: blue : yellow : red : green. How many times would each colour be expected?

6.In Harrison’s actual 24 spins, the wheel lands on blue 10 times and yellow 8 times. Write the experimental ratio blue : yellow in simplest form. Is it the same as the wheel’s theoretical ratio?

7.The other 6 spins were red or green. If 4 were red, how many were green? Write the experimental ratio red : green in simplest form.

8.A friend says, “Yellow came up 8 times, so yellow must be more likely than blue.” Use both the spinner ratio and Harrison’s results to explain why this conclusion is not reliable.

9.The stall owner wants a wheel where winning a small prize (blue or yellow) and winning a bonus prize (red or green) are in the ratio 3:1. Does the current wheel meet this target? Show the ratio in simplest form.

10.To make the bonus prize twice as likely as before while keeping 12 equal sectors, the owner changes the wheel to 4 blue, 2 yellow, 4 red and 2 green sectors. Compare the new bonus-to-small-prize ratio with the original wheel, which has 6 blue, 3 yellow, 2 red and 1 green sector. Has the chance of a bonus prize doubled?